SOLUTION: The perimeter of a rectangle is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle.

Question 152203: The perimeter of a rectangle is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle.
Answer by orca(409) (Show Source): You can put this solution on YOUR website!
Let the length and width of the rectangle be x and y respectively.
As the perimeter of a rectangle is 44, we have
2x + 2y = 44 ......(1)
As the area of the rectangle is 117, we have
xy = 117 ........(2)
Simplifying equation (1), we have
x + y = 22 .......(3)
Solving the following simultaneous equations for x and y.
x + y = 22
xy = 117
Substituting y = 22 - x into xy = 117,we have
x(22 - x) = 117
22x - x^2 = 117
x^2 - 22x + 117 = 0
(x - 9)(x - 13) = 0
So x = 9 or x = 13
Substituting x = 9 into y = 22 - x,we have y = 13.
Substituting x = 13 into y = 22 - x,we have y = 9.
So the dimensions of the rectangle are 9 and 13.

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